A principal component analysis for trees
Copyright policy )A principal component analysis for trees
The active field of Functional Data Analysis (about understanding the variation in a set of curves) has been recently extended to Object Oriented Data Analysis, which considers populations of more general objects. A particularly challenging extension of this set of ideas is to populations of tree-structured objects. We develop an analog of Principal Component Analysis for trees, based on the notion of tree-lines, and propose numerically fast (linear time) algorithms to solve the resulting optimization problems. The solutions we obtain are used in the analysis of a data set of 73 individuals, where each data object is a tree of blood vessels in one person's brain.
- University of North Carolina at Chapel Hill United States
- Colorado State University United States
- UNIVERSITY OF NORTH CAROLINA CHAPEL HILL
- University of North Carolina at Greensboro United States
FOS: Computer and information sciences, tree-structured objects, principal component analysis, Applications of graph theory, Computational problems in statistics, population structure, Mathematics - Statistics Theory, Statistics Theory (math.ST), Factor analysis and principal components; correspondence analysis, tree-lines, Quantitative Biology - Quantitative Methods, Statistics - Computation, Applications of statistics to biology and medical sciences; meta analysis, Optimization and Control (math.OC), Object oriented data analysis, FOS: Biological sciences, object oriented data analysis, 62H99, 62G99, 05C05, 9008, FOS: Mathematics, Mathematics - Optimization and Control, Quantitative Methods (q-bio.QM), Computation (stat.CO)
FOS: Computer and information sciences, tree-structured objects, principal component analysis, Applications of graph theory, Computational problems in statistics, population structure, Mathematics - Statistics Theory, Statistics Theory (math.ST), Factor analysis and principal components; correspondence analysis, tree-lines, Quantitative Biology - Quantitative Methods, Statistics - Computation, Applications of statistics to biology and medical sciences; meta analysis, Optimization and Control (math.OC), Object oriented data analysis, FOS: Biological sciences, object oriented data analysis, 62H99, 62G99, 05C05, 9008, FOS: Mathematics, Mathematics - Optimization and Control, Quantitative Methods (q-bio.QM), Computation (stat.CO)
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